2. Insurance Company An insurance company states that 90% of its claims are settled within 30...

2. Insurance Company An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a random sample of 75 of the company's claims to test this statement. If the consumer group found that 55 of the claims were settled within 30 days, do they have sufficient reason to support their contention that fewer than 90% of the claims are settled within 30 days? Use 0.05 level of significance. Hint: We are testing for population proportion (single sample). When we look from the consumer group’s perspective, we would like to see if the proportion of claims settled within 30 days is less than 90%. Therefore, the null hypothesis states H0: P=0.9, where the alternative hypothesis states H1: P<0.9, indicating a left tailed test.

Expert Solution

= 55/75 = 0.733

The test statistic is

At , the critical value is -z0.05 = -1.645

Since the test statistic value is less than the critical value, so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that fewer than 90% of the claims are settled within 30 days.

orchestra answered 2 years ago

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